Problem: Simplify the following expression: $z = \dfrac{8n^2 - 8n - 96}{n - 4} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $8$ , so we can rewrite the expression: $ z =\dfrac{8(n^2 - 1n - 12)}{n - 4} $ Then we factor the remaining polynomial: $n^2 {-1}n {-12} $ ${-4} + {3} = {-1}$ ${-4} \times {3} = {-12}$ $ (n {-4}) (n + {3}) $ This gives us a factored expression: $\dfrac{8(n {-4}) (n + {3})}{n - 4}$ We can divide the numerator and denominator by $(n + 4)$ on condition that $n \neq 4$ Therefore $z = 8(n + 3); n \neq 4$